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Solvability of an inverse problem for discontinuous Sturm–Liouville operators
Author(s) -
Zhang Ran,
Bondarenko Natalia Pavlovna,
Yang Chuan Fu
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6713
Subject(s) - sturm–liouville theory , mathematics , eigenfunction , boundary value problem , uniqueness , mathematical analysis , operator (biology) , inverse , inverse problem , uniqueness theorem for poisson's equation , interval (graph theory) , oscillation (cell signaling) , eigenvalues and eigenvectors , jump , combinatorics , geometry , biochemistry , physics , chemistry , genetics , repressor , quantum mechanics , biology , transcription factor , gene
In this paper, we consider the Sturm–Liouville equation with the jump conditions inside the interval (0, π ). The inverse problem is studied, which consists in recovering operator coefficients from two spectra, corresponding to different boundary conditions. We prove the uniqueness theorem and provide necessary and sufficient conditions for solvability of the inverse problem. We also obtain the oscillation theorem for the eigenfunctions of the considered discontinuous boundary value problem.